The formal definition is: Another interpretation is that modular arithmetic deals with all the integers, but divide them into N equivalence classes, each of the form {i + kN ∣ k ∈ Z} {i + k N ∣ …

Dec 3, 2024 · This is fairly common to use when you need to move back and forth between integer and modular arithmetic. In particular, programming languages usually have such an …

I know how to solve mod using division i.e. $$11 \\mod 7 = 4$$ For this I did a simple division and took its remainder: i.e. $$11 = 7 \\cdot 1 + 4$$ Where $11$ was dividend, $7$ divisor, $1$ …

The reason that equivalence class arithmetic proves smoother is that congruence mod m is not only an equivalence relation but is, additionally, an arithmetic congruence relation, i.e. it …

Modular arithmetic (clock arithmetic) is a system of integer arithmetic based on the congruence relation a ≡ b (mod n) a ≡ b (mod n) which means that n n divides a − b a b.

Sep 4, 2017 · My question is rather simple as I'm interested about modulus and multiplication, specifically whether it holds that $(a*b)\\,mod\\,n=(a\\,mod\\,n)*(b\\,mod\\,n)$?

Jan 9, 2013 · I was wondering what would happen if we tried to do a modulo operand with complex numbers? For instance, what would be the answer (if any) to the next statement? $ x …

Mar 31, 2015 · Yes, this is certainly something one can talk about. But first, let's look at normal modular arithmetic. If m, n ∈Z m, n ∈ Z, you can talk about m (mod n) m (mod n). Often, we …

Dec 25, 2023 · Perhaps the best question to start with is " Can modular arithmetic be extended to the rational or real numbers?", which leads us to "What is modular arithmetic?", which I like to …

Aug 15, 2018 · I had a doubt regarding the ‘mod’ operator So far I thought that modulus referred to the remainder, for example $8 \\mod 6 = 2$ The same way, $6 \\mod 8 = 6$, since $8\\cdot …